A digital animation studio rents two web servers, A and B, by the hour from a cloud computing provider. Each month, depending on production needs of different projects at the studio, the animation studio uses each of the two web servers for a random amount of time. The monthly usage of server A is normally distributed with a mean of 200 hours and a standard deviation 30. The monthly usage of server B is normally distributed with a mean of 400 hours and standard deviation of 70 hours. The monthly usage of server A is known to have a correlation of -0.8 with the monthly usage of server B. Use of server A is billed at a cost of $100 per hour to the studio, while use of server B is billed at a cost of $80 per hour to the studio.

a) Find the expected value of the total monthly server usage in hours billed to the studio. (10 points)

b) Find the expected value of the total monthly cost to the studio arising from the use of the two servers.

c) Calculate the covariance between the monthly usage in hours of server A and the monthly usage in hours of server B. (10 points)

d) Find the standard deviation of the total monthly server usage in hours billed to the studio.

e) Find the standard deviation of the total monthly cost to the studio arising from the use of the two servers. (15 points)

f) What is the probability that the total monthly cost to the studio arising from the two servers exceeds $60,000?